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10. Using the converse of the alternate interior angle theorem, we can prove that line J is parallel to line K.

Given:

[tex]\angle\text{ 16 }\cong\text{ }\angle\text{ 10}[/tex]

Prove: J || K

Statement:

[tex]\angle\text{ 16 }\cong\text{ }\angle\text{ 10 }[/tex]

Reason: Given

Statement:

[tex]\angle\text{ 10 }\cong\text{ }\angle\text{ 12 }[/tex]

Reason: Vertical angles theorem

Statement:

[tex]\angle\text{ 12 }\cong\text{ }\angle\text{ 16}[/tex]

Reason: Transitive property of congruence

Statement:

J || K

Reason:

[tex]\text{Converse of the corresponding angles postulate}[/tex]

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